Can I blur images "the other way?
With a little encouragement from @Rich Sedman, copied from comment:
The white square looks bigger, because of the conversion after compositing to sRGB for your display device. Arithmetically, inside the compositor, the squares are the same size. If you go to Color Management and switch the View Transform to 'Raw', you can see that.
You could use gamma correction after blurring in the compositor, to change that, but you would have to be be aware, that were you to use the squares for masking or suchlike, that part of the pipeline would become non-linear.